Reduction of State-to-State to Macroscopic Models for Hypersonics

Four different types of macroscopic models developed for the vibration-chemistry coupling in nonequilibrium flows for re-entry applications are presented. First, using an approach based on nonequilibrium thermodynamics, global rate coefficients of dissociation of N2 and O2 under parent molecular or atomic impact and backward molecular recombination are determined. Then a Two-Level Distribution (TLD) model is developed, in which a relaxation equation for vibrational temperature is solved as in the case of multi-temperature models but with the simultaneous solution of a kinetic equation, as in the case of state-to-state models, but only for the last vibrational level. In a third approach, a multi-internal temperature model is presented to describe accurately the vibrational distribution function in using several groups of levels, within which the levels are assumed to follow a Boltzmann distribution at an internal temperature of the group. This multi-internal temperature model allows us to describe accurately the vibrational energy relaxation and dissociation processes behind a strong shock wave. Finally, a rovibrational collisional coarse-grain model is developed to reduce a detailed rovibrational mechanism for the internal energy excitation and dissociation processes behind a strong shock wave in a nitrogen flow.